Periodic solutions for a class of reaction–diffusion equations with p-Laplacian

In this paper we study non-trivial, non-negative periodic solutions of certain periodic reaction–diffusion equations with the pp-Laplacian under the homogeneous Dirichlet boundary condition. First, we prove the existence of such periodic solutions, and provide a priori estimates for their upper bound using Moser iteration. We also show that the support of these solutions is independent of time. Further, we establish the attractivity of maximal periodic solutions using the monotonicity method. One of our motivations is a generalized Verhulst model with time-periodicity and nonlinear diffusion in a bounded heterogeneous environment.